The delivery of carefully-planned doses of radiation may be used to treat various medical conditions. For example, radiation treatments are used, often in conjunction with other treatments, in the treatment and control of certain cancers. While it can be beneficial to deliver appropriate amounts of radiation to certain structures or tissues, in general, radiation can harm living tissue. It is desirable to target radiation on a target volume containing the structures or tissues to be irradiated while minimizing the dose of radiation delivered to surrounding tissues. Intensity modulated radiation therapy (IMRT) is one method that has been used to deliver radiation to target volumes in living subjects.
IMRT typically involves delivering shaped radiation beams from a few different directions. The radiation beams are typically delivered in sequence. The radiation beams each contribute to the desired dose in the target volume.
A typical radiation delivery apparatus has a source of radiation, such as a linear accelerator, and a rotatable gantry. The gantry can be rotated to cause a radiation beam to be incident on a subject from various different angles. The shape of the incident radiation beam can be modified by a multi-leaf collimator (MLC). A MLC has a number of leaves which are mostly opaque to radiation. The MLC leaves define an aperture through which radiation can propagate. The positions of the leaves can be adjusted to change the shape of the aperture and to thereby shape the radiation beam that propagates through the MLC. The MLC may also be rotatable to different angles.
Objectives associated with radiation treatment for a subject typically specify a three-dimensional distribution of radiation dose that it is desired to deliver to a target region within the subject. The desired dose distribution typically specifies dose values for voxels located within the target. Ideally, no radiation would be delivered to tissues outside of the target region. In practice, however, objectives associated with radiation treatment may involve specifying a maximum acceptable dose that may be delivered to tissues outside of the target.
Treatment planning involves identifying an optimal (or at least acceptable) set of parameters for delivering radiation to a particular treatment volume. Treatment planning is not a trivial problem. The problem that treatment planning seeks to solve involves a wide range of variables including:                the three-dimensional configuration of the treatment volume;        the desired dose distribution within the treatment volume;        the locations and radiation tolerance of tissues surrounding the treatment volume; and        constraints imposed by the design of the radiation delivery apparatus.The possible solutions also involve a large number of variables including:        the number of beam directions to use;        the direction of each beam;        the shape of each beam; and        the amount of radiation delivered in each beam.        
Various conventional methods of treatment planning are described in:                S. V. Spirou and C.-S. Chui. A gradient inverse planning algorithm with dose-volume constraints, Med. Phys. 25, 321-333 (1998);        Q. Wu and R. Mohand. Algorithm and functionality of an intensity modulated radiotherapy optimization system, Med. Phys. 27, 701-711 (2000);        S. V. Spirou and C.-S. Chui. Generation of arbitrary intensity profiles by dynamic jaws or multileaf collimators, Med. Phys. 21, 1031-1041 (1994);        P. Xia and L. J. Verhey. Multlleaf collimator leaf sequencing algorithm for intensity modulated beams with multiple static segments, Med. Phys. 25, 1424-1434 (1998); and        K. Otto and B. G. Clark. Enhancement of IMRT delivery through MLC rotation,” Phys. Med. Biol. 47, 3997-4017 (2002).        
Acquiring sophisticated modern radiation treatment apparatus, such as a linear accelerator, can involve significant capital cost. Therefore it is desirable to make efficient use of such apparatus. All other factors being equal, a radiation treatment plan that permits a desired distribution of radiation dose to be delivered in a shorter time is preferable to a radiation treatment plan that requires a longer time to deliver. A treatment plan that can be delivered in a shorter time permits more efficient use of the radiation treatment apparatus. A shorter treatment plan also reduces the risk that a subject will move during delivery of the radiation in a manner that may significantly impact the accuracy of the delivered dose.
Despite the advances that have been made in the field of radiation therapy, there remains a need for radiation treatment methods and apparatus and radiation treatment planning methods and apparatus that provide improved control over the delivery of radiation, especially to complicated target volumes. There also remains a need for such methods and apparatus that can deliver desired dose distributions relatively quickly.